On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups

On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups Full article

Journal

Ricerche di Matematica
ISSN: 0035-5038 , E-ISSN: 1827-3491

Output data

Year: 2024, Volume: 74, Pages: 61–78 Pages count : 18 DOI: 10.1007/s11587-024-00847-8

Tags

Simple group · Group with abelian Sylow 2-subgroups · Small Ree group · Sporadic Janko group · Spectrum of a group · Recognition by spectrum

Authors

Li Tao ¹ , Moghaddamfar A.R. ² , Vasil’ev A.V. ³ , Zhigang Wang ¹

Affiliations

1	School of Mathematics and Statistics, Hainan University, Haikou, Hainan, People’s Republic of China
2	Faculty of Mathematics, K. N. Toosi University of Technology, P. O. Box 16765-3381, Tehran, Iran
3	Sobolev Institute of Mathematics, Novosibirsk, Russia, 630090

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0002

The spectrum of a group is the set of orders of its elements. Finite groups with the same spectra as the direct squares of the finite simple groups with abelian Sylow 2subgroups are considered. It is proved that the direct square J1 × J1 of the sporadic Janko group J1 andthedirectsquares2G2(q)×2G2(q)of the simple small Ree groups 2G2(q) are uniquely characterized by their spectra in the class of finite groups, while for the direct square PSL2(q) × PSL2(q) of a 2-dimensional simple linear group PSL2(q), there are always infinitely many groups (even solvable groups) with the same spectra.

Li T. , Moghaddamfar A.R. , Vasil’ev A.V. , Zhigang W.
On recognition of the direct squares of the simple groups with abelian Sylow 2-subgroups
Ricerche di Matematica. 2024. V.74. P.61–78. DOI: 10.1007/s11587-024-00847-8 WOS Scopus РИНЦ OpenAlex

Submitted:	Dec 13, 2023
Accepted:	Jan 2, 2024
Published online:	Feb 1, 2024

Web of science:	WOS:001154424400001
Scopus:	2-s2.0-85183697480
Elibrary:	65981417
OpenAlex:	W4391423517

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